Integrands of loop amplitudes within loop-tree duality
Robert L. Runkel, Zoltán Szőr, Juan Pablo Vesga, Stefan Weinzierl
Abstract
Using loop-tree duality, we relate a renormalized $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularized $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show that up to three loops the latter object is easily computable from recurrence relations. This defines an integrand of the loop amplitude with a global definition of the loop momenta. Field and mass renormalization are performed in the on-shell scheme.
Topics & Concepts
Loop (graph theory)Duality (order theory)RenormalizationAmplitudeQuantum field theoryPhysicsMathematical physicsTree (set theory)MathematicsField theory (psychology)Scattering amplitudeQuantum electrodynamicsQuantum mechanicsMathematical analysisPure mathematicsCombinatoricsBlack Holes and Theoretical PhysicsParticle physics theoretical and experimental studiesCosmology and Gravitation Theories